Shahab Haghi - Academia.edu (original) (raw)

Papers by Shahab Haghi

Discussiones Mathematicae Graph Theory, 2014

A subset S of vertices in a graph G is called a total irredundant set if, for each vertex v in G,... more A subset S of vertices in a graph G is called a total irredundant set if, for each vertex v in G, v or one of its neighbors has no neighbor in S − {v}. The total irredundance number, ir(G), is the minimum cardinality of a maximal total irredundant set of G, while the upper total irredundance number, IR(G), is the maximum cardinality of a such set. In this paper we characterize all cubic graphs G with ir t (G) = IR t (G) = 2.

Discussiones Mathematicae Graph Theory, 2018

For two graphs G 1 and G 2 , the Ramsey number R(G 1 , G 2) is the smallest integer N , such that... more For two graphs G 1 and G 2 , the Ramsey number R(G 1 , G 2) is the smallest integer N , such that for any graph on N vertices, either G contains G 1 or G contains G 2. Let S n be a star of order n and W m be a wheel of order m + 1. In this paper, we will show R(W n , S n) ≤ 5n/2 − 1, where n ≥ 6 is even. Also, by using this theorem, we conclude that R(W n , S n) = 5n/2 − 2 or 5n/2 − 1, for n ≥ 6 and even. Finally, we prove that for sufficiently large even n we have R(W n , S n) = 5n/2 − 2.

Discussiones Mathematicae Graph Theory, 2017

A tree containing exactly two non-pendant vertices is called a doublestar. A double-star with deg... more A tree containing exactly two non-pendant vertices is called a doublestar. A double-star with degree sequence (k 1 + 1, k 2 + 1, 1,. .. , 1) is denoted by S k1,k2. We study the edge-decomposition of graphs into double-stars. It was proved that every double-star of size k decomposes every 2k-regular graph. In this paper, we extend this result by showing that every graph in which every vertex has degree 2k + 1 or 2k + 2 and containing a 2-factor is decomposed into S k1,k2 and S k1−1,k2 , for all positive integers k 1 and k 2 such that k 1 + k 2 = k.

arXiv (Cornell University), May 20, 2015

A tree containing exactly two non-pendant vertices is called a double-star. A double-star with de... more A tree containing exactly two non-pendant vertices is called a double-star. A double-star with degree sequence (k 1 + 1, k 2 + 1, 1,. .. , 1) is denoted by S k1,k2. We study the edge-decomposition of regular graphs into double-stars. It was proved that every double-star of size k decomposes every 2k-regular graph. In this paper, we extend this result to (2k + 1)-regular graphs, by showing that every (2k + 1)-regular graph containing two disjoint perfect matchings is decomposed into S k1,k2 and S k1−1,k2 , for all positive integers k 1 and k 2 such that k 1 + k 2 = k.

arXiv (Cornell University), May 20, 2015

A tree containing exactly two non-pendant vertices is called a double-star. A double-star with de... more A tree containing exactly two non-pendant vertices is called a double-star. A double-star with degree sequence (k 1 + 1, k 2 + 1, 1,. .. , 1) is denoted by S k1,k2. We study the edge-decomposition of regular graphs into double-stars. It was proved that every double-star of size k decomposes every 2k-regular graph. In this paper, we extend this result to (2k + 1)-regular graphs, by showing that every (2k + 1)-regular graph containing two disjoint perfect matchings is decomposed into S k1,k2 and S k1−1,k2 , for all positive integers k 1 and k 2 such that k 1 + k 2 = k.

Discrete Applied Mathematics, 2017

For two graphs G and H, the Ramsey number r(G, H) is the smallest positive integer r, such that a... more For two graphs G and H, the Ramsey number r(G, H) is the smallest positive integer r, such that any red/blue coloring of the edges of graph K r contains either a red subgraph that is isomorphic to G or a blue subgraph that is isomorphic to H. Let S k = K 1,k be a star of order k + 1 and K n ⊔ S k be a graph obtained by adding a new vertex v and joining v to k vertices of K n. The star-critical Ramsey number r * (G, H) is the smallest positive integer k such that any red/blue coloring of the edges of graph K r−1 ⊔ S k contains either a red subgraph that is isomorphic to G or a blue subgraph that is isomorphic to H where r = r(G, H). In this paper, it is shown that r * (F n , K 4) = 4n + 2 where n ≥ 4.

Discussiones Mathematicae Graph Theory, 2017

A tree containing exactly two non-pendant vertices is called a doublestar. A double-star with deg... more A tree containing exactly two non-pendant vertices is called a doublestar. A double-star with degree sequence (k 1 + 1, k 2 + 1, 1,. .. , 1) is denoted by S k1,k2. We study the edge-decomposition of graphs into double-stars. It was proved that every double-star of size k decomposes every 2k-regular graph. In this paper, we extend this result by showing that every graph in which every vertex has degree 2k + 1 or 2k + 2 and containing a 2-factor is decomposed into S k1,k2 and S k1−1,k2 , for all positive integers k 1 and k 2 such that k 1 + k 2 = k.

Discussiones Mathematicae Graph Theory, 2017

For two graphs G 1 and G 2 , the Ramsey number R(G 1 , G 2) is the smallest integer N , such that... more For two graphs G 1 and G 2 , the Ramsey number R(G 1 , G 2) is the smallest integer N , such that for any graph on N vertices, either G contains G 1 or G contains G 2. Let S n be a star of order n and W m be a wheel of order m + 1. In this paper, we will show R(W n , S n) ≤ 5n/2 − 1, where n ≥ 6 is even. Also, by using this theorem, we conclude that R(W n , S n) = 5n/2 − 2 or 5n/2 − 1, for n ≥ 6 and even. Finally, we prove that for sufficiently large even n we have R(W n , S n) = 5n/2 − 2.

Discussiones Mathematicae Graph Theory, 2014

A subset S of vertices in a graph G is called a total irredundant set if, for each vertex v in G,... more A subset S of vertices in a graph G is called a total irredundant set if, for each vertex v in G, v or one of its neighbors has no neighbor in S − {v}. The total irredundance number, ir(G), is the minimum cardinality of a maximal total irredundant set of G, while the upper total irredundance number, IR(G), is the maximum cardinality of a such set. In this paper we characterize all cubic graphs G with ir t (G) = IR t (G) = 2.

Discussiones Mathematicae Graph Theory, 2018

For two graphs G 1 and G 2 , the Ramsey number R(G 1 , G 2) is the smallest integer N , such that... more For two graphs G 1 and G 2 , the Ramsey number R(G 1 , G 2) is the smallest integer N , such that for any graph on N vertices, either G contains G 1 or G contains G 2. Let S n be a star of order n and W m be a wheel of order m + 1. In this paper, we will show R(W n , S n) ≤ 5n/2 − 1, where n ≥ 6 is even. Also, by using this theorem, we conclude that R(W n , S n) = 5n/2 − 2 or 5n/2 − 1, for n ≥ 6 and even. Finally, we prove that for sufficiently large even n we have R(W n , S n) = 5n/2 − 2.

Discussiones Mathematicae Graph Theory, 2017

A tree containing exactly two non-pendant vertices is called a doublestar. A double-star with deg... more A tree containing exactly two non-pendant vertices is called a doublestar. A double-star with degree sequence (k 1 + 1, k 2 + 1, 1,. .. , 1) is denoted by S k1,k2. We study the edge-decomposition of graphs into double-stars. It was proved that every double-star of size k decomposes every 2k-regular graph. In this paper, we extend this result by showing that every graph in which every vertex has degree 2k + 1 or 2k + 2 and containing a 2-factor is decomposed into S k1,k2 and S k1−1,k2 , for all positive integers k 1 and k 2 such that k 1 + k 2 = k.

arXiv (Cornell University), May 20, 2015

A tree containing exactly two non-pendant vertices is called a double-star. A double-star with de... more A tree containing exactly two non-pendant vertices is called a double-star. A double-star with degree sequence (k 1 + 1, k 2 + 1, 1,. .. , 1) is denoted by S k1,k2. We study the edge-decomposition of regular graphs into double-stars. It was proved that every double-star of size k decomposes every 2k-regular graph. In this paper, we extend this result to (2k + 1)-regular graphs, by showing that every (2k + 1)-regular graph containing two disjoint perfect matchings is decomposed into S k1,k2 and S k1−1,k2 , for all positive integers k 1 and k 2 such that k 1 + k 2 = k.

arXiv (Cornell University), May 20, 2015

A tree containing exactly two non-pendant vertices is called a double-star. A double-star with de... more A tree containing exactly two non-pendant vertices is called a double-star. A double-star with degree sequence (k 1 + 1, k 2 + 1, 1,. .. , 1) is denoted by S k1,k2. We study the edge-decomposition of regular graphs into double-stars. It was proved that every double-star of size k decomposes every 2k-regular graph. In this paper, we extend this result to (2k + 1)-regular graphs, by showing that every (2k + 1)-regular graph containing two disjoint perfect matchings is decomposed into S k1,k2 and S k1−1,k2 , for all positive integers k 1 and k 2 such that k 1 + k 2 = k.

Discrete Applied Mathematics, 2017

For two graphs G and H, the Ramsey number r(G, H) is the smallest positive integer r, such that a... more For two graphs G and H, the Ramsey number r(G, H) is the smallest positive integer r, such that any red/blue coloring of the edges of graph K r contains either a red subgraph that is isomorphic to G or a blue subgraph that is isomorphic to H. Let S k = K 1,k be a star of order k + 1 and K n ⊔ S k be a graph obtained by adding a new vertex v and joining v to k vertices of K n. The star-critical Ramsey number r * (G, H) is the smallest positive integer k such that any red/blue coloring of the edges of graph K r−1 ⊔ S k contains either a red subgraph that is isomorphic to G or a blue subgraph that is isomorphic to H where r = r(G, H). In this paper, it is shown that r * (F n , K 4) = 4n + 2 where n ≥ 4.

Discussiones Mathematicae Graph Theory, 2017

A tree containing exactly two non-pendant vertices is called a doublestar. A double-star with deg... more A tree containing exactly two non-pendant vertices is called a doublestar. A double-star with degree sequence (k 1 + 1, k 2 + 1, 1,. .. , 1) is denoted by S k1,k2. We study the edge-decomposition of graphs into double-stars. It was proved that every double-star of size k decomposes every 2k-regular graph. In this paper, we extend this result by showing that every graph in which every vertex has degree 2k + 1 or 2k + 2 and containing a 2-factor is decomposed into S k1,k2 and S k1−1,k2 , for all positive integers k 1 and k 2 such that k 1 + k 2 = k.

Discussiones Mathematicae Graph Theory, 2017

For two graphs G 1 and G 2 , the Ramsey number R(G 1 , G 2) is the smallest integer N , such that... more For two graphs G 1 and G 2 , the Ramsey number R(G 1 , G 2) is the smallest integer N , such that for any graph on N vertices, either G contains G 1 or G contains G 2. Let S n be a star of order n and W m be a wheel of order m + 1. In this paper, we will show R(W n , S n) ≤ 5n/2 − 1, where n ≥ 6 is even. Also, by using this theorem, we conclude that R(W n , S n) = 5n/2 − 2 or 5n/2 − 1, for n ≥ 6 and even. Finally, we prove that for sufficiently large even n we have R(W n , S n) = 5n/2 − 2.